Mass-Spring Project

by Michele Houtappels

2012

Math 1060 – TrigonometryInstructor: Zeph Smith

Michele Houtappels Math 1060

October 27, 2012

Modeling the Motion of a Spring Project Reflection

Some important everyday life examples of mass-spring systems are around us all of the time. For instance, the spring in a car’s shock absorber assembly which allows us to have a comfortable and safe ride and there’s the trampoline in which the mass-spring system gives it its bounce when someone jumps on it. Bungee cords are also another example as well as a pendulum of a clock. Even, humans and animal’s musculoskeletal system works as a mass-spring system which has a leg spring and a mass. And of course, there are the many rides at an amusement park that are built and operate with this type of system. It is important to know the amplitude, period and frequency of these systems. If these were not known we could have some serious issues. For instance, if the amplitude, distance from equilibrium, of the bounce was not known, the mass-spring system would increase and decrease outside of the safe distance causing harm or most likely death in the case of a bungee cord jumper or an amusement park visitor. Also, we wouldn’t want the shock absorbers of a car to continue to bounce. In the case of a pendulum, it moves back and forth repeating in a given period with a certain amplitude. The frequency is how often something happens in a certain amount of time. Frequency is not the same as same as period, which is how long it takes to complete one cycle. All of this information is important to know in order for an object to function safely and as expected. This project did change how I think about trigonometry and the real world. There are so many factors to consider when something is manufactured, along with many other things in our universe. To be able to approach these issues in a mathematical way is truly amazing. Especially using trigonometry to measure the amplitude, period, shifts, velocity, angles and other factors. You can even estimate the size of something without even being there!

Thank You